What is the experimental setup used to count photons from a laser or even a lamp? Of course, in the case of the lamp, I would be able to count only the photons that pass through an area sensor in a particular observation point.

If at all possible, a setup that can be done at home is preferred--one that avoids expensive instruments as much as possible (I may be crazy to even think this is possible). The key point is:

We can't count photons like we count sheep. So how do we infer from the effects of single photons and count from there?

I can start with $E = \frac{hc}{\lambda}$, and all other manifestations of energy, like heat or motion.

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A single photon can easily be detected by a photomultiplier. The basic idea is that a photon hitting a metal plate in the tube ejects an electron from the metal plate by the photoelectric effect. An electric field inside the photomultiplier then accelerates the electron until it slams into another metal plate, releasing a bunch of electrons. These are then accelerated to a third metal plate, etc. The end result is a sizable current we can measure. The Wikipedia article is quite good and has more detail. You might be able to build a crude one at home with a lot of dedication, but it's a delicate device requiring a vacuum and quality electronics. These devices work for IR to UV light.

We can also measure individual photons with a scintillation counter. I used these in a couple of undergraduate labs to detect x-ray radiation from nuclear processes. They work by detecting when a photon (usually high-energy) ionizes an atom in some particular substrate, so they're tuned to detect photons at certain ranges of frequencies. The scintillator does not directly detect these photons, but converts them to several lower-energy photons that we can detect with other means to infer the high-energy photons' presence, so you'll need some more electronics to go with it. Still, we were able to watch single-photon events get counted in lab. (Thanks dmckee for clarification in comments).

One device you can fairly easily build at home is a cloud chamber, but it will detect mostly $\alpha$ and $\beta$ radiation rather than photons. However, you might see trails from high-energy photons (gamma radiation). There should be lots of sets of instructions on the web for how to build one.

Nice, but I'm going to quibble about the scintillator: that's a mechanism to generate a bunch of lower energy (usually visible band) photons from one high energy one. Then you go about counting the visible photons with a PMT, MCP, or high QE photodiode. It might be better to talk about ionization detectors (Geiger tubes, proportional tubes and more sophisticated wire chambers) in that context.
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dmckee♦Feb 8 '11 at 20:40

The eye photoreceptors will react to a single photon (ie the rhodopsin in the rods), but the brain will not register it. It needs around 5 or so to register in consciousness.
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Gordon Feb 8 '11 at 22:04

@dmckee: So the scintillator is some sort of down-converter?
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KitFeb 9 '11 at 1:04

@Kit: Scintillators convert some of the energy lost by ionizing particles passing through them into light. High energy photons scatter electrons along their path, and it's their energy that the scintillator responds to.
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dmckee♦Feb 9 '11 at 2:31

A good CCD camera basically works at the single photon level.
Amateur astronomers who photograph faint stars by stacking images are working at this level.
You can get more info from Sky & Telescope or Astronomy magazines.

+1 for CCDs. Even the cheap one can respond to single photons, but their quantum efficiency is not impressive.
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dmckee♦Feb 8 '11 at 20:41

Would it be possible to add a link showing how good a CCD camera is? That would answer the questioner's question on home brew single photon counters. I'll +1 when I see the addition.
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Carl BrannenFeb 12 '11 at 0:44

The right graph shows a measurement that was taken on a camera with 1 electron per pixel read noise: physics.stackexchange.com/questions/12058/…. The gain used in this experiment wasn't maximum. If you can live with low dynamic range -- you'll have to if you want to see single photons -- you can increase the EM gain by maybe a factor 20. But then CIC (clock induced charge) is an important problem. If you can live with 100kHz readout speed you can use a cheap CCD camera. I tried this one: starlight-xpress.co.uk/products.htm.
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whoplispJul 9 '11 at 10:00